Penalized Multimarker vs. Single-Marker Regression Methods for Genome-Wide Association Studies of Quantitative Traits

The data from genome-wide association studies (GWAS) in humans are still predominantly analyzed using single-marker association methods. As an alternative to single-marker analysis (SMA), all or subsets of markers can be tested simultaneously. This approach requires a form of penalized regression (PR) as the number of SNPs is much larger than the sample size. Here we review PR methods in the context of GWAS, extend them to perform penalty parameter and SNP selection by false discovery rate (FDR) control, and assess their performance in comparison with SMA. PR methods were compared with SMA, using realistically simulated GWAS data with a continuous phenotype and real data. Based on these comparisons our analytic FDR criterion may currently be the best approach to SNP selection using PR for GWAS. We found that PR with FDR control provides substantially more power than SMA with genome-wide type-I error control but somewhat less power than SMA with Benjamini–Hochberg FDR control (SMA-BH). PR with FDR-based penalty parameter selection controlled the FDR somewhat conservatively while SMA-BH may not achieve FDR control in all situations. Differences among PR methods seem quite small when the focus is on SNP selection with FDR control. Incorporating linkage disequilibrium into the penalization by adapting penalties developed for covariates measured on graphs can improve power but also generate more false positives or wider regions for follow-up. We recommend the elastic net with a mixing weight for the Lasso penalty near 0.5 as the best method.     

Genome Wide Association Studies Using a New Nonparametric Model Reveal the Genetic Architecture of 17 Agronomic Traits in an Enlarged Maize Association Panel

Association mapping is a powerful approach for dissecting the genetic architecture of complex quantitative traits using high-density SNP markers in maize. Here, we expanded our association panel size from 368 to 513 inbred lines with 0.5 million high quality SNPs using a two-step data-imputation method which combines identity by descent (IBD) based projection and k-nearest neighbor (KNN) algorithm. Genome-wide association studies (GWAS) were carried out for 17 agronomic traits with a panel of 513 inbred lines applying both mixed linear model (MLM) and a new method, the Anderson-Darling (A-D) test. Ten loci for five traits were identified using the MLM method at the Bonferroni-corrected threshold −log₁₀ (P) >5.74 (α = 1). Many loci ranging from one to 34 loci (107 loci for plant height) were identified for 17 traits using the A-D test at the Bonferroni-corrected threshold −log₁₀ (P) >7.05 (α = 0.05) using 556809 SNPs. Many known loci and new candidate loci were only observed by the A-D test, a few of which were also detected in independent linkage analysis. This study indicates that combining IBD based projection and KNN algorithm is an efficient imputation method for inferring large missing genotype segments. In addition, we showed that the A-D test is a useful complement for GWAS analysis of complex quantitative traits. Especially for traits with abnormal phenotype distribution, controlled by moderate effect loci or rare variations, the A-D test balances false positives and statistical power. The candidate SNPs and associated genes also provide a rich resource for maize genetics and breeding.     

Iterative Usage of Fixed and Random Effect Models for Powerful and Efficient Genome-Wide Association Studies

False positives in a Genome-Wide Association Study (GWAS) can be effectively controlled by a fixed effect and random effect Mixed Linear Model (MLM) that incorporates population structure and kinship among individuals to adjust association tests on markers; however, the adjustment also compromises true positives. The modified MLM method, Multiple Loci Linear Mixed Model (MLMM), incorporates multiple markers simultaneously as covariates in a stepwise MLM to partially remove the confounding between testing markers and kinship. To completely eliminate the confounding, we divided MLMM into two parts: Fixed Effect Model (FEM) and a Random Effect Model (REM) and use them iteratively. FEM contains testing markers, one at a time, and multiple associated markers as covariates to control false positives. To avoid model over-fitting problem in FEM, the associated markers are estimated in REM by using them to define kinship. The P values of testing markers and the associated markers are unified at each iteration. We named the new method as Fixed and random model Circulating Probability Unification (FarmCPU). Both real and simulated data analyses demonstrated that FarmCPU improves statistical power compared to current methods. Additional benefits include an efficient computing time that is linear to both number of individuals and number of markers. Now, a dataset with half million individuals and half million markers can be analyzed within three days.     

Efficient control of population structure in model organism association mapping

Genomewide association mapping in model organisms such as inbred mouse strains is a promising approach for the identification of risk factors related to human diseases. However, genetic association studies in inbred model organisms are confronted by the problem of complex population structure among strains. This induces inflated false positive rates, which cannot be corrected using standard approaches applied in human association studies such as genomic control or structured association. Recent studies demonstrated that mixed models successfully correct for the genetic relatedness in association mapping in maize and Arabidopsis panel data sets. However, the currently available mixed-model methods suffer from computational inefficiency. In this article, we propose a new method, efficient mixed-model association (EMMA), which corrects for population structure and genetic relatedness in model organism association mapping. Our method takes advantage of the specific nature of the optimization problem in applying mixed models for association mapping, which allows us to substantially increase the computational speed and reliability of the results. We applied EMMA to in silico whole-genome association mapping of inbred mouse strains involving hundreds of thousands of SNPs, in addition to Arabidopsis and maize data sets. We also performed extensive simulation studies to estimate the statistical power of EMMA under various SNP effects, varying degrees of population structure, and differing numbers of multiple measurements per strain. Despite the limited power of inbred mouse association mapping due to the limited number of available inbred strains, we are able to identify significantly associated SNPs, which fall into known QTL or genes identified through previous studies while avoiding an inflation of false positives. An R package implementation and webserver of our EMMA method are publicly available.     

Comparison of Methods to Account for Relatedness in Genome-Wide Association Studies with Family-Based Data

Approaches based on linear mixed models (LMMs) have recently gained popularity for modelling population substructure and relatedness in genome-wide association studies. In the last few years, a bewildering variety of different LMM methods/software packages have been developed, but it is not always clear how (or indeed whether) any newly-proposed method differs from previously-proposed implementations. Here we compare the performance of several LMM approaches (and software implementations, including EMMAX, GenABEL, FaST-LMM, Mendel, GEMMA and MMM) via their application to a genome-wide association study of visceral leishmaniasis in 348 Brazilian families comprising 3626 individuals (1972 genotyped). The implementations differ in precise details of methodology implemented and through various user-chosen options such as the method and number of SNPs used to estimate the kinship (relatedness) matrix. We investigate sensitivity to these choices and the success (or otherwise) of the approaches in controlling the overall genome-wide error-rate for both real and simulated phenotypes. We compare the LMM results to those obtained using traditional family-based association tests (based on transmission of alleles within pedigrees) and to alternative approaches implemented in the software packages MQLS, ROADTRIPS and MASTOR. We find strong concordance between the results from different LMM approaches, and all are successful in controlling the genome-wide error rate (except for some approaches when applied naively to longitudinal data with many repeated measures). We also find high correlation between LMMs and alternative approaches (apart from transmission-based approaches when applied to SNPs with small or non-existent effects). We conclude that LMM approaches perform well in comparison to competing approaches. Given their strong concordance, in most applications, the choice of precise LMM implementation cannot be based on power/type I error considerations but must instead be based on considerations such as speed and ease-of-use.     

Accurate haplotype inference for multiple linked single-nucleotide polymorphisms using sibship data

Sibships are commonly used in genetic dissection of complex diseases, particularly for late-onset diseases. Haplotype-based association studies have been advocated as powerful tools for fine mapping and positional cloning of complex disease genes. Existing methods for haplotype inference using data from relatives were originally developed for pedigree data. In this study, we proposed a new statistical method for haplotype inference for multiple tightly linked single-nucleotide polymorphisms (SNPs), which is tailored for extensively accumulated sibship data. This new method was implemented via an expectation-maximization (EM) algorithm without the usual assumption of linkage equilibrium among markers. Our EM algorithm does not incur extra computational burden for haplotype inference using sibship data when compared with using unrelated parental data. Furthermore, its computational efficiency is not affected by increasing sibship size. We examined the robustness and statistical performance of our new method in simulated data created from an empirical haplotype data set of human growth hormone gene 1. The utility of our method was illustrated with an application to the analyses of haplotypes of three candidate genes for osteoporosis.     

A multi-layer method to study genome-scale positions of nucleosomes

The basic unit of eukaryotic chromatin is the nucleosome, consisting of about 150 bp of DNA wrapped around a protein core made of histone proteins. Nucleosomes position is modulated in vivo to regulate fundamental nuclear processes. To measure nucleosome positions on a genomic scale both theoretical and experimental approaches have been recently reported. We have developed a new method, Multi-Layer Model (MLM), for the analysis of nucleosome position data obtained with microarray-based approach. The MLM is a feature extraction method in which the input data is processed by a classifier to distinguish between several kinds of patterns. We applied our method to simulated-synthetic and experimental nucleosome position data and found that besides a high nucleosome recognition and a strong agreement with standard statistical methods, the MLM can identify distinct classes of nucleosomes, making it an important tool for the genome wide analysis of nucleosome position and function. In conclusion, the MLM allows a better representation of nucleosome position data and a significant reduction in computational time.     

Multiple interval mapping for gene expression QTL analysis

To find the correlations between genome-wide gene expression variations and sequence polymorphisms in inbred cross populations, we developed a statistical method to claim expression quantitative trait loci (eQTL) in a genome. The method is based on multiple interval mapping (MIM), a model selection procedure, and uses false discovery rate (FDR) to measure the statistical significance of the large number of eQTL. We compared our method with a similar procedure proposed by Storey et al. and found that our method can be more powerful. We identified the features in the two methods that resulted in different statistical powers for eQTL detection, and confirmed them by simulation. We organized our computational procedure in an R package which can estimate FDR for positive findings from similar model selection procedures. The R package, MIM-eQTL, can be found at .     

Candidate genes versus genome-wide associations: which are better for detecting genetic susceptibility to infectious disease?

Technological developments allow increasing numbers of markers to be deployed in case-control studies searching for genetic factors that influence disease susceptibility. However, with vast numbers of markers, true 'hits' may become lost in a sea of false positives. This problem may be particularly acute for infectious diseases, where the control group may contain unexposed individuals with susceptible genotypes. To explore this effect, we used a series of stochastic simulations to model a scenario based loosely on bovine tuberculosis. We find that a candidate gene approach tends to have greater statistical power than studies that use large numbers of single nucleotide polymorphisms (SNPs) in genome-wide association tests, almost regardless of the number of SNPs deployed. Both approaches struggle to detect genetic effects when these are either weak or if an appreciable proportion of individuals are unexposed to the disease when modest sample sizes (250 each of cases and controls) are used, but these issues are largely mitigated if sample sizes can be increased to 2000 or more of each class. We conclude that the power of any genotype-phenotype association test will be improved if the sampling strategy takes account of exposure heterogeneity, though this is not necessarily easy to do.     

Selecting tagging SNPs for association studies using power calculations from genotype data

Recent studies have indicated that linkage disequilibrium (LD) between single nucleotide polymorphism (SNP) markers can be used to derive a reduced set of tagging SNPs (tSNPs) for genetic association studies. Previous strategies for identifying tSNPs have focused on LD measures or haplotype diversity, but the statistical power to detect disease-associated variants using tSNPs in genetic studies has not been fully characterized. We propose a new approach of selecting tSNPs based on determining the set of SNPs with the highest power to detect association. Two-locus genotype frequencies are used in the power calculations. To show utility, we applied this power method to a large number of SNPs that had been genotyped in Caucasian samples. We demonstrate that a significant reduction in genotyping efforts can be achieved although the reduction depends on genotypic relative risk, inheritance mode and the prevalence of disease in the human population. The tSNP sets identified by our method are remarkably robust to changes in the disease model when small relative risk and additive mode of inheritance are employed. We have also evaluated the ability of the method to detect unidentified SNPs. Our findings have important implications in applying tSNPs from different data sources in association studies.     

Integration Analysis of Three Omics Data Using Penalized Regression Methods: An Application to Bladder Cancer

Omics data integration is becoming necessary to investigate the genomic mechanisms involved in complex diseases. During the integration process, many challenges arise such as data heterogeneity, the smaller number of individuals in comparison to the number of parameters, multicollinearity, and interpretation and validation of results due to their complexity and lack of knowledge about biological processes. To overcome some of these issues, innovative statistical approaches are being developed. In this work, we propose a permutation-based method to concomitantly assess significance and correct by multiple testing with the MaxT algorithm. This was applied with penalized regression methods (LASSO and ENET) when exploring relationships between common genetic variants, DNA methylation and gene expression measured in bladder tumor samples. The overall analysis flow consisted of three steps: (1) SNPs/CpGs were selected per each gene probe within 1Mb window upstream and downstream the gene; (2) LASSO and ENET were applied to assess the association between each expression probe and the selected SNPs/CpGs in three multivariable models (SNP, CPG, and Global models, the latter integrating SNPs and CPGs); and (3) the significance of each model was assessed using the permutation-based MaxT method. We identified 48 genes whose expression levels were significantly associated with both SNPs and CPGs. Importantly, 36 (75%) of them were replicated in an independent data set (TCGA) and the performance of the proposed method was checked with a simulation study. We further support our results with a biological interpretation based on an enrichment analysis. The approach we propose allows reducing computational time and is flexible and easy to implement when analyzing several types of omics data. Our results highlight the importance of integrating omics data by applying appropriate statistical strategies to discover new insights into the complex genetic mechanisms involved in disease conditions.     

Enhanced statistical tests for GWAS in admixed populations: assessment using African Americans from CARe and a Breast Cancer Consortium

While genome-wide association studies (GWAS) have primarily examined populations of European ancestry, more recent studies often involve additional populations, including admixed populations such as African Americans and Latinos. In admixed populations, linkage disequilibrium (LD) exists both at a fine scale in ancestral populations and at a coarse scale (admixture-LD) due to chromosomal segments of distinct ancestry. Disease association statistics in admixed populations have previously considered SNP association (LD mapping) or admixture association (mapping by admixture-LD), but not both. Here, we introduce a new statistical framework for combining SNP and admixture association in case-control studies, as well as methods for local ancestry-aware imputation. We illustrate the gain in statistical power achieved by these methods by analyzing data of 6,209 unrelated African Americans from the CARe project genotyped on the Affymetrix 6.0 chip, in conjunction with both simulated and real phenotypes, as well as by analyzing the FGFR2 locus using breast cancer GWAS data from 5,761 African-American women. We show that, at typed SNPs, our method yields an 8% increase in statistical power for finding disease risk loci compared to the power achieved by standard methods in case-control studies. At imputed SNPs, we observe an 11% increase in statistical power for mapping disease loci when our local ancestry-aware imputation framework and the new scoring statistic are jointly employed. Finally, we show that our method increases statistical power in regions harboring the causal SNP in the case when the causal SNP is untyped and cannot be imputed. Our methods and our publicly available software are broadly applicable to GWAS in admixed populations.     

Haplotype block structure and its applications to association studies: power and study designs

Recent studies have shown that the human genome has a haplotype block structure, such that it can be divided into discrete blocks of limited haplotype diversity. In each block, a small fraction of single-nucleotide polymorphisms (SNPs), referred to as "tag SNPs," can be used to distinguish a large fraction of the haplotypes. These tag SNPs can potentially be extremely useful for association studies, in that it may not be necessary to genotype all SNPs; however, this depends on how much power is lost. Here we develop a simulation study to quantitatively assess the power loss for a variety of study designs, including case-control designs and case-parental control designs. First, a number of data sets containing case-parental or case-control samples are generated on the basis of a disease model. Second, a small fraction of case and control individuals in each data set are genotyped at all the loci, and a dynamic programming algorithm is used to determine the haplotype blocks and the tag SNPs based on the genotypes of the sampled individuals. Third, the statistical power of tests was evaluated on the basis of three kinds of data: (1) all of the SNPs and the corresponding haplotypes, (2) the tag SNPs and the corresponding haplotypes, and (3) the same number of randomly chosen SNPs as the number of tag SNPs and the corresponding haplotypes. We study the power of different association tests with a variety of disease models and block-partitioning criteria. Our study indicates that the genotyping efforts can be significantly reduced by the tag SNPs, without much loss of power. Depending on the specific haplotype block-partitioning algorithm and the disease model, when the identified tag SNPs are only 25% of all the SNPs, the power is reduced by only 4%, on average, compared with a power loss of approximately 12% when the same number of randomly chosen SNPs is used in a two-locus haplotype analysis. When the identified tag SNPs are approximately 14% of all the SNPs, the power is reduced by approximately 9%, compared with a power loss of approximately 21% when the same number of randomly chosen SNPs is used in a two-locus haplotype analysis. Our study also indicates that haplotype-based analysis can be much more powerful than marker-by-marker analysis.     

A Graphical Weighted Power Improving Multiplicity Correction Approach for SNP Selections

Controlling for the multiplicity effect is an essential part of determining statistical significance in large-scale single-locus association genome scans on Single Nucleotide Polymorphisms (SNPs). Bonferroni adjustment is a commonly used approach due to its simplicity, but is conservative and has low power for large-scale tests. The permutation test, which is a powerful and popular tool, is computationally expensive and may mislead in the presence of family structure. We propose a computationally efficient and powerful multiple testing correction approach for Linkage Disequilibrium (LD) based Quantitative Trait Loci (QTL) mapping on the basis of graphical weighted-Bonferroni methods. The proposed multiplicity adjustment method synthesizes weighted Bonferroni-based closed testing procedures into a powerful and versatile graphical approach. By tailoring different priorities for the two hypothesis tests involved in LD based QTL mapping, we are able to increase power and maintain computational efficiency and conceptual simplicity. The proposed approach enables strong control of the familywise error rate (FWER). The performance of the proposed approach as compared to the standard Bonferroni correction is illustrated by simulation and real data. We observe a consistent and moderate increase in power under all simulated circumstances, among different sample sizes, heritabilities, and number of SNPs. We also applied the proposed method to a real outbred mouse HDL cholesterol QTL mapping project where we detected the significant QTLs that were highlighted in the literature, while still ensuring strong control of the FWER.     

Multi-locus test conditional on confirmed effects leads to increased power in genome-wide association studies

Complex diseases or phenotypes may involve multiple genetic variants and interactions between genetic, environmental and other factors. Current genome-wide association studies (GWAS) mostly used single-locus analysis and had identified genetic effects with multiple confirmations. Such confirmed single-nucleotide polymorphism (SNP) effects were likely to be true genetic effects and ignoring this information in testing new effects of the same phenotype results in decreased statistical power due to increased residual variance that has a component of the omitted effects. In this study, a multi-locus association test (MLT) was proposed for GWAS analysis conditional on SNPs with confirmed effects to improve statistical power. Analytical formulae for statistical power were derived and were verified by simulation for MLT accounting for confirmed SNPs and for single-locus test (SLT) without accounting for confirmed SNPs. Statistical power of the two methods was compared by case studies with simulated and the Framingham Heart Study (FHS) GWAS data. Results showed that the MLT method had increased statistical power over SLT. In the GWAS case study on four cholesterol phenotypes and serum metabolites, the MLT method improved statistical power by 5% to 38% depending on the number and effect sizes of the conditional SNPs. For the analysis of HDL cholesterol (HDL-C) and total cholesterol (TC) of the FHS data, the MLT method conditional on confirmed SNPs from GWAS catalog and NCBI had considerably more significant results than SLT.     

Power for detecting genetic divergence: differences between statistical methods and marker loci

Information on statistical power is critical when planning investigations and evaluating empirical data, but actual power estimates are rarely presented in population genetic studies. We used computer simulations to assess and evaluate power when testing for genetic differentiation at multiple loci through combining test statistics or P values obtained by four different statistical approaches, viz. Pearson's chi-square, the log-likelihood ratio G-test, Fisher's exact test, and an F(ST)-based permutation test. Factors considered in the comparisons include the number of samples, their size, and the number and type of genetic marker loci. It is shown that power for detecting divergence may be substantial for frequently used sample sizes and sets of markers, also at quite low levels of differentiation. The choice of statistical method may be critical, though. For multi-allelic loci such as microsatellites, combining exact P values using Fisher's method is robust and generally provides a high resolving power. In contrast, for few-allele loci (e.g. allozymes and single nucleotide polymorphisms) and when making pairwise sample comparisons, this approach may yield a remarkably low power. In such situations chi-square typically represents a better alternative. The G-test without Williams's correction frequently tends to provide an unduly high proportion of false significances, and results from this test should be interpreted with great care. Our results are not confined to population genetic analyses but applicable to contingency testing in general.     

Genome-wide selection of tag SNPs using multiple-marker correlation

MOTIVATIONS: The tag SNP approach is a valuable tool in whole genome association studies, and a variety of algorithms have been proposed to identify the optimal tag SNP set. Currently, most tag SNP selection is based on two-marker (pairwise) linkage disequilibrium (LD). Recent literature has shown that multiple-marker LD also contains useful information that can further increase the genetic coverage of the tag SNP set. Thus, tag SNP selection methods that incorporate multiple-marker LD are expected to have advantages in terms of genetic coverage and statistical power. RESULTS: We propose a novel algorithm to select tag SNPs in an iterative procedure. In each iteration loop, the SNP that captures the most neighboring SNPs (through pair-wise and multiple-marker LD) is selected as a tag SNP. We optimize the algorithm and computer program to make our approach feasible on today's typical workstations. Benchmarked using HapMap release 21, our algorithm outperforms standard pair-wise LD approach in several aspects. (i) It improves genetic coverage (e.g. by 7.2% for 200 K tag SNPs in HapMap CEU) compared to its conventional pair-wise counterpart, when conditioning on a fixed tag SNP number. (ii) It saves genotyping costs substantially when conditioning on fixed genetic coverage (e.g. 34.1% saving in HapMap CEU at 90% coverage). (iii) Tag SNPs identified using multiple-marker LD have good portability across closely related ethnic groups and (iv) show higher statistical power in association tests than those selected using conventional methods. AVAILABILITY: A computer software suite, multiTag, has been developed based on this novel algorithm. The program is freely available by written request to the author at ke_hao@merck.com     

Estimating missing heritability for disease from genome-wide association studies

Genome-wide association studies are designed to discover SNPs that are associated with a complex trait. Employing strict significance thresholds when testing individual SNPs avoids false positives at the expense of increasing false negatives. Recently, we developed a method for quantitative traits that estimates the variation accounted for when fitting all SNPs simultaneously. Here we develop this method further for case-control studies. We use a linear mixed model for analysis of binary traits and transform the estimates to a liability scale by adjusting both for scale and for ascertainment of the case samples. We show by theory and simulation that the method is unbiased. We apply the method to data from the Wellcome Trust Case Control Consortium and show that a substantial proportion of variation in liability for Crohn disease, bipolar disorder, and type I diabetes is tagged by common SNPs.     

Number of SNPS loci needed to detect population structure

The study of the association of polymorphic genetic markers with common diseases is one of the most powerful tools in modern genetics. Interest in single nucleotide polymorphisms (SNPs) has steadily grown over the last decade. SNPs are currently the most developed markers in the human genome because they have a number of advantages over other marker types. One of the critical problems responsible for 'spurious' association findings in case-control studies is population stratification. There are many statistical approaches developed for detecting population heterogeneity. However the power to detect population structure by known methods is highly dependent on the number of loci utilised. We performed an analysis of SNPs data available in the public domain from The Single Nucleotide Consortia Ltd. (TSCL). Three populations, Afro-American, Asian and Caucasian, were compared. Estimation of the minimum number of SNPs loci necessary for detection of the population structure was performed. Two clustering approaches, distance-based and model-based, were compared. The model-based approach was superior when compared with the distance-based method. We found more than 65 random SNPs loci are required for identifying distinct geographically separated populations. Increasing the number of markers to over 100 raises the probability of correct assignment of a particular individual to an origin group to over 90%, even with conventional clustering methods.     

Conditional Random Fields for Fast, Large-Scale Genome-Wide Association Studies

Understanding the role of genetic variation in human diseases remains an important problem to be solved in genomics. An important component of such variation consist of variations at single sites in DNA, or single nucleotide polymorphisms (SNPs). Typically, the problem of associating particular SNPs to phenotypes has been confounded by hidden factors such as the presence of population structure, family structure or cryptic relatedness in the sample of individuals being analyzed. Such confounding factors lead to a large number of spurious associations and missed associations. Various statistical methods have been proposed to account for such confounding factors such as linear mixed-effect models (LMMs) or methods that adjust data based on a principal components analysis (PCA), but these methods either suffer from low power or cease to be tractable for larger numbers of individuals in the sample. Here we present a statistical model for conducting genome-wide association studies (GWAS) that accounts for such confounding factors. Our method scales in runtime quadratic in the number of individuals being studied with only a modest loss in statistical power as compared to LMM-based and PCA-based methods when testing on synthetic data that was generated from a generalized LMM. Applying our method to both real and synthetic human genotype/phenotype data, we demonstrate the ability of our model to correct for confounding factors while requiring significantly less runtime relative to LMMs. We have implemented methods for fitting these models, which are available at http://www.microsoft.com/science.